Outage Probability Conjecture for TIMO channels

Let $P>0$, let $f(q_1,q_2)$ denote the outage-probability expression obtained for a two-transmit-antenna, $r$-receive-antenna channel with nonnegative powers $q_1,q_2$, and define

$$\mathcal{D}=\{(q_1,q_2)\in[0,P]^2\mid q_1+q_2=P\}.$$

Outage Probability Conjecture for TIMO. The pairs $(q_1,q_2)$ minimizing $f(q_1,q_2)$ over $\mathcal{D}$ belong to

$$\left\{(P,0),\left(\frac{P}{2},\frac{P}{2}\right),(0,P)\right\}.$$

This is the two-transmit-antenna specialization of the general outage probability conjecture. The paper presents a counterexample in its TIMO analysis, so the stated conjecture is refuted.